Module:Powharmonic series

Module documentation[view] [edit] [history] [purge]

This module should not be invoked directly; use its corresponding template instead: Template:Powharmonic series.

This module generates a table showing the intervals of a powharmonic series for a given exponent, which is used to model timbres involving stretched or compressed harmonics.

Introspection summary for Module:Powharmonic series
Functions provided (1) Line Function Params 3 powharmonic (invokable) (frame)	Lua modules required (0) Variable Module Functions used

No function descriptions were provided. The Lua code may have further information.

---

local p = {}

function p.powharmonic(frame)
    local n = tonumber(frame.args["n"])
    local expo = tonumber(frame.args["expo"])
    local out_str = "{| class=\"wikitable\"\n" ..
	    "|+ Intervals of the " .. expo .. "-Powharmonic series\n" ..
	    "! rowspan=\"2\" | Pitch #\n" ..
	    "! colspan=\"2\" | Frequency multiplier\n" ..
	    "! colspan=\"3\" | Pitch\n" ..
	    "|-\n" ..
	    "! Definition\n" ..
	    "! Decimal\n" ..
	    "! Cents\n" ..
	    "! Change (cents)\n" ..
	    "! Octave-reduced\n"
    local fmt_mul = string.format("%%.%df", tonumber(frame.args["prec"]))
    local fmt_cent = "%.2f"
    local p_prev = 0
    local p_current = 0

    for i = 1, n do
        p_current = 1200 * math.log(i) / math.log(2) * expo
        out_str = out_str ..
            "|-\n" ..
            "| " .. i .. "\n" ..
            "| " .. i .. "<sup>" .. expo .. "</sup>\n" ..
            "| " .. string.format(fmt_mul, i^expo) .. "\n" ..
            "| " .. string.format(fmt_cent, p_current) .. "\n" ..
            "| " .. string.format(fmt_cent, p_current - p_prev) .. "\n" ..
            "| " .. string.format(fmt_cent, math.fmod(p_current, 1200)) .. "\n"
        p_prev = p_current
    end

    out_str = out_str .. "|}"
    return out_str
end

return p